Upper End of the War

[Daimos]

Vasilys war analysis is impressive. I rate it 5 stars. Please conitue.

[Natan]

Nuts to you, here come statistics!

The probability of a successful nuke through an SDI on a single try is 40%. Not favorable, but not terrible. However, the probability of getting a nuke through in two tries jumps to 64%.

1-(1/p(x))^n, where p(x) is the probability of a successful nuke and n is the number of attempts. So we get 1-0.6^n. I threw that into Excel to see the probability of a nuke landing in up to 10 shots.

Rounded to the tenths as necessary...
1 = 40%
2 = 64%
3 = 78.4%
4 = 87.0%
5 = 92.2%
6 = 95.3%
7 = 97.2%
8 = 98.3%
9 = 99.0%
10 = 99.0%

On the average, your nuke should probably get through by the second attempt. But the average isn't what we usually notice or get miffed about. We get frustrated with (or extremely grateful for) SDIs when they block nuke after nuke after nuke. So what's the chance of an SDI blocking n nukes in a row? It's just the inverse of above: 0.6^n

Rounded to the tenths as necessary...
1 = 60%
2 = 36%
3 = 21.6%
4 = 13.0%
5 = 7.8%
6 = 4.7%
7 = 2.8%
8 = 1.7%
9 = 1.0%
10 = 0.1%

A nearly 8% chance of blocking 5 nukes in a row is not negligible. In a month of war (1v1), it's all but guaranteed to happen to you at least once, probably when you're already low on nukes. But that's much preferable to 1v2s and 1v3s; in the last of those, if you're trying to nuke everybody everyday, you're going to run out of nukes. And the 5 block rock isn't alone; the chances of an SDI blocking 4 or 6 nukes in a row is similarly non-negligible and would require 1/5 or more of a full stockpile to land one damn nuke.

This plays a huge influence in how each side fights the war and underpins macro-scale strategies.

 

I can't wait for someone who really doesn't understand probability to reply to this
 

[dem61s]

Nuts to you, here come statistics!

The probability of a successful nuke through an SDI on a single try is 40%. Not favorable, but not terrible. However, the probability of getting a nuke through in two tries jumps to 64%.

1-(1/p(x))^n, where p(x) is the probability of a successful nuke and n is the number of attempts. So we get 1-0.6^n. I threw that into Excel to see the probability of a nuke landing in up to 10 shots.

Rounded to the tenths as necessary...
1 = 40%
2 = 64%
3 = 78.4%
4 = 87.0%
5 = 92.2%
6 = 95.3%
7 = 97.2%
8 = 98.3%
9 = 99.0%
10 = 99.0%

On the average, your nuke should probably get through by the second attempt. But the average isn't what we usually notice or get miffed about. We get frustrated with (or extremely grateful for) SDIs when they block nuke after nuke after nuke. So what's the chance of an SDI blocking n nukes in a row? It's just the inverse of above: 0.6^n

Rounded to the tenths as necessary...
1 = 60%
2 = 36%
3 = 21.6%
4 = 13.0%
5 = 7.8%
6 = 4.7%
7 = 2.8%
8 = 1.7%
9 = 1.0%
10 = 0.1%

A nearly 8% chance of blocking 5 nukes in a row is not negligible. In a month of war (1v1), it's all but guaranteed to happen to you at least once, probably when you're already low on nukes. But that's much preferable to 1v2s and 1v3s; in the last of those, if you're trying to nuke everybody everyday, you're going to run out of nukes. And the 5 block rock isn't alone; the chances of an SDI blocking 4 or 6 nukes in a row is similarly non-negligible and would require 1/5 or more of a full stockpile to land one damn nuke.

This plays a huge influence in how each side fights the war and underpins macro-scale strategies.

 

Nooooooo! The probability to hit in 10 attempts or less should read 99.4%, not 99.0% !!!

Clearly, this changes everything!

 

[CubaQuerida]

Unless you are in Umbrella where your chances of blocking a nuke become:

1: 8%
2: 3%
3: 1.02%
4: 0.03%
5+: 21%

Just from personal observation.

[dem61s]

Unless you are in Umbrella where your chances of blocking a nuke become:

1: 8%
2: 3%
3: 1.02%
4: 0.03%
5+: 21%

Just from personal observation.

 

Serious stats right here.

[enderland]

The only issue I see with that is that EQ's reserves are falling off.  You're right about bringing more stockpiles to the table, however if you look at Doomhouse front to keep all 58 of the nations you face in anarchy you'd need your peace mode reserves to average 1.6 wars.  Or in more simple terms, 22 of your 36 reserve nations would need to declare two wars.  

 

This is of course a bit of an oversimplification in that it assumes every one of your nations currently in war mode will be in anarchy and unable to declare on a target.  It's an assumption, but not one I'd say is insane in that anarchy is widespread when the nukes fly.

 

That means you'll have 22 nations that enter the war with 25 nukes each, can buy 12 during the war, and need to fire 12.  So 25 of 37 can be sponged up by the SDI and you get your hit a day.  You can tolerate a 68% intercept rate on those.  So 22 of your 36 nations can tolerate a 68%.  The other 14 can tolerate a 84% intercept rate.

 

The issue is if your reserves continue to drop off you reach a point where your reserves need to average 2.3 wars or something like that your intercept rate tolerance drops too low and you can't launch a nuke a day.  Meanwhile rearming will take 13 days assuming the nation is WRC capable.  When a nation enters a war without a full stockpile instead of it being 25 out of 37 can miss or 31 out of 37 can miss.  Suddenly it say 16 out of 22 can miss (72% intercept rate), 10 out of 22 (45% intercept rate), etc.  

 

Of course you can also alter the odds by shorting the number of days a nation needs to fire nukes for.  Have a nation say fire for four days and then have a second nation declare and take over.  That just means that second nation comes into the war early and has less time to rebuild the stockpile.  

 

I see the looming issue for the EQ forces fighting on some fronts being the stockpile they bring into the table and the intercept rate they can tolerate.  Your reserves are dropping off while DH has achieved parity.  If we reach a point where say both sides are averaging being hit by two nukes per war cycle, it swings in favor of Umbrella.  They get to hit you twice with a nuke that has 12k tech behind it, you get to hit them twice by a nuke that only have 7k tech behind it.  I bet a lot of Umbrella nations will take that deal.  

 

Basically I'm not sure if you can keep doing 3 v 1 with all three of your guys having full nuclear stockpiles.  EQ can push the odds in the direction of 3 v 1 in the TOP front, but if they do so that means no nations sitting back and reloading the silo which spells trouble in a round or two depending on how many nations have to shoot themselves dry to crack the SDIs.  On the other fronts, I'm not seeing how you get 3 v 1 above 100k.  Of course below it, 3 v 1 is manageable in a number of tiers.  

 

Edit:

Oh and we almost made it page 5 before things started degenerating.  I guess that counts for something.  

There are a variety of factors to consider here. Even a small numeric superiority on the part of EQ can end up as a significant advantage in a longer term war (and vice versa).

1. As DH nations are forced to remain in war mode, they will slowly (or quickly, depending on how many nations attack them) end up with a depleted nuke stockpile. At this point when nukes are at zero,  there will be an average of 0.8 nukes a day landing from the DH side on EQ nations from each depleted nation. Each of these nations is likely to be receiving a nuke each day as well, so on an individual level, the ratio of nukes from EQ to DH will be roughly 0.8:1 if all wars are 1v1
2. The only real meaningful damage will be from tech quite quickly (because how cheap infra is from 0-1k or even 5k) for large nations
3. Because of this, aircraft become pointless (in the 1k infra range rebuying aircraft is financially pointless, you could lose 1k infra and it's still cheaper to just rebuy the 1k infra than to continue to restock airforce) other than to boost NS
4. Likewise, meaningful damage from CMs becomes nearly exclusively tech damage
5. Each Equilibrium nation which is able to "escape" to peace mode or just not having wars can rebuy 10+ nukes
6. A nation requires approx. 2.5 nukes to "hit" another nation
7. A nation starting with 25 nukes will have 25 + 7*2 = 39 nukes to use (note: rebuying the first day only happens if a nuke is spied) which is just under an average of 16 successful nuclear attacks statistically for a week of war
8. A war can land 7 nukes (if you declare early enough) which means a nation starting from 25 nukes can expect, statistically, to be able to nuke two other nations continuously for the duration

Now. From this, consider:

1. A single EQ nation with maximum nukes can drop 2x as many nukes as it can receive if declaring solo wars against 2 DH nations (and, even if tech is off a factor of 2x, cause roughly equal total tech damage, absorbing slightly more due to additional CMs and possibly more due to GAs).  Note that while each individual DH nation can land 0.8 nukes individually, both defending nations have this chance. So they most often will land a successful return nuke.
2. This strategy requires only 1/2 as many EQ nations to be engaged as DH nations from an optimal sense (all declaring two offensive wars)

In this situation, if numbers of nations in each NS bracket are approximately equal to begin with, optimally EQ nations will be able to rearm up to at least 14 nukes before needing to reneter the fight to continue to keep nations in anarchy and receiving a nuke a day. This is just not sufficient to nuke daily (you need to start with roughly 16-18 to be able to do this against two nations, as you effectively lose 3 a day from starting stockpile).

 

If EQ maintains numeric superiority in nations in each NS bracket, it becomes quite maintainable (and easy) to do this sort of rotation, and consistently cause more tech damage to the DH side with only a slight numeric advantage. The keys, for whichever side will "win" are maintaining

• ability to restock nuclear supplies whether through no defensive wars or peacemode
• morale of players going through the "grind"
• morale of players going INTO the "grind"
• an advantage in deployment and/or numbers (though deployment is more significant than straight numerical superiority, as seen above)
• opponent's nations from reaching peace mode
• nations in range of majority of opposite side

Of course, there's nothing preventing the exact opposite in NS ranges where DH has the advantage in either deployment or numbers (specifically the upper tier).

[AntyCrist]

Nuts to you, here come statistics!

The probability of a successful nuke through an SDI on a single try is 40%. Not favorable, but not terrible. However, the probability of getting a nuke through in two tries jumps to 64%.

1-(1/p(x))^n, where p(x) is the probability of a successful nuke and n is the number of attempts. So we get 1-0.6^n. I threw that into Excel to see the probability of a nuke landing in up to 10 shots.

Rounded to the tenths as necessary...
1 = 40%
2 = 64%
3 = 78.4%
4 = 87.0%
5 = 92.2%
6 = 95.3%
7 = 97.2%
8 = 98.3%
9 = 99.0%
10 = 99.0%

On the average, your nuke should probably get through by the second attempt. But the average isn't what we usually notice or get miffed about. We get frustrated with (or extremely grateful for) SDIs when they block nuke after nuke after nuke. So what's the chance of an SDI blocking n nukes in a row? It's just the inverse of above: 0.6^n

Rounded to the tenths as necessary...
1 = 60%
2 = 36%
3 = 21.6%
4 = 13.0%
5 = 7.8%
6 = 4.7%
7 = 2.8%
8 = 1.7%
9 = 1.0%
10 = 0.1%

A nearly 8% chance of blocking 5 nukes in a row is not negligible. In a month of war (1v1), it's all but guaranteed to happen to you at least once, probably when you're already low on nukes. But that's much preferable to 1v2s and 1v3s; in the last of those, if you're trying to nuke everybody everyday, you're going to run out of nukes. And the 5 block rock isn't alone; the chances of an SDI blocking 4 or 6 nukes in a row is similarly non-negligible and would require 1/5 or more of a full stockpile to land one damn nuke.

This plays a huge influence in how each side fights the war and underpins macro-scale strategies.

  Slighlty more deateal than I ment (and Im not a fan of your notation) it miss one point.  the expected value of 6 rounds and 3 targets is 3(6)p=18(0.4)=7.2 with a sd of rad(npq)=rad(18(0.4)(0.6))=rad(18(0.24)) jest more than 2

so 5-9 nucks landed totle for 3+ targets .

 

[Ardus]

Nooooooo! The probability to hit in 10 attempts or less should read 99.4%, not 99.0% !!!

Clearly, this changes everything!

 

You're right; my bad.  Was distracted.

[dem61s]

You're right; my bad.  Was distracted.

 

And I was bored enough that I actually checked your calculations. I think the joke is on me. ;_;

[shahenshah]

I wonder that DH side are trying/will try to rebuild their former high tier nations who are nuked under 100k to avoid staggers? Making a big infra jump like that isn't crazy, but actually you could avoid a lot of damage if you have 1 stagger, not 3 guy who coordinate declare on you. Clearly a lot of nations on DH side could afford that, but i haven't really seen anyone using that so far.

One of my target burned through 1 bn buying back stuff. That was 25% of his wc. I think he figured the trade off wasnt good as he fell back in the range in he bought out of again and now is doing the usual. Still, I think this could be used at later stage when there is more exhaustion. Tho there are some crazy wcs on both sides.

[Unknown Smurf]

Good strategy on paper but its not turning out that way, and even if you have SDI, the nukes still sting a lot. There just aren't enough nations to serve as fodder for the hi tech nations, and unfortunately tech cannot be rebought by the thousands. The real question becomes "are there enough nations willing to have themselves fully destroyed week after week?" Umbrella doesn't really have a choice in the matter.

Yes but they can only get 2 nukes per day.. at best considering SDIs will block some. 

[CubaQuerida]

Yes but they can only get 2 nukes per day.. at best considering SDIs will block some. 

My final thought on this is that not all targets are being solo'd here, and in my particular case, I am not always the nuker, even if I have the most tech.  At the highest end of this war, it's a bit more lopsided as far as who can nuke who, and while yes, I can only buy 2 nukes, some days I don't even have to use more than 1.

 

The nukes do run out eventually I suppose but so much damage is being done by them that I don't even find it necessary to nuke every day, especially if the target is turtling.  Again, very specific cases here, and every war is different.

 

Personally I despise the tactic of just "throwing nations" at high tech/low infra nation just for the sake of keeping them in anarchy, only to do comparatively low damage.  I've been on both sides of it, and neither one is especially rewarding.  It's only the third week of this war too, :)  A lot more action to come I'm sure of it.

[Longshadow]

Personally I despise the tactic of just "throwing nations" at high tech/low infra nation just for the sake of keeping them in anarchy, only to do comparatively low damage.  I've been on both sides of it, and neither one is especially rewarding.  It's only the third week of this war too, :)  A lot more action to come I'm sure of it.

You should try talking sense into Kaskus then. :lol1:

 

But seriously I've never seen a more interesting war than this one, and I've seen several big coalition wars.

[Unknown Smurf]

You should try talking sense into Kaskus then. :lol1:

 

But seriously I've never seen a more interesting war than this one, and I've seen several big coalition wars.

Hmm..? Isn't NPOs strategy to just throw nations at us? Correct me if I'm wrong... but either way we're not throwing ourselves into high tech nations. If anything, its the opposite.

[Longshadow]

Hmm..? Isn't NPOs strategy to just throw nations at us? Correct me if I'm wrong... but either way we're not throwing ourselves into high tech nations. If anything, its the opposite.

 

You should read his post better, being on either side (aka the one being the high tech nation or the one being the low tech nation) wins.

[D34th]

Please, keep your stupid war with Kaskus out of this thread.

Edited February 2, 2013 by D34th

[Namayan]

Can you make the same analysis as your original post but this time the time would be recently to compare how is the war faring statistically compared to the last time you analyzed it on your first post? You may also compare if your analysis on the matter is correct compared to the actual results. This should tell us a rough indication on what is happening or where is the war leaning to which side.

[AntyCrist]

I suport thiss holehartedly

Can you make the same analysis as your original post but this time the time would be recently to compare how is the war faring statistically compared to the last time you analyzed it on your first post? You may also compare if your analysis on the matter is correct compared to the actual results. This should tell us a rough indication on what is happening or where is the war leaning to which side.

 

[rabonnobar]

Can you make the same analysis as your original post but this time the time would be recently to compare how is the war faring statistically compared to the last time you analyzed it on your first post? You may also compare if your analysis on the matter is correct compared to the actual results. This should tell us a rough indication on what is happening or where is the war leaning to which side.

 

I'd also like for OP to do this, but you should take a look at my blog too: http://forums.cybernations.net/index.php?/blog/811/entry-3662-stats-itb-3/

[Charles Stuart]

Hmm..? Isn't NPOs strategy to just throw nations at us? Correct me if I'm wrong... but either way we're not throwing ourselves into high tech nations. If anything, its the opposite.

 

 

Who is this us?

[Oranges]

Hmm..? Isn't NPOs strategy to just throw nations at us? Correct me if I'm wrong... but either way we're not throwing ourselves into high tech nations. If anything, its the opposite.

 

Shit guys, he's on to us. We better start fighting srsly lolz :awesome:

Edited February 5, 2013 by Oranges

[Saladjoe]

Excellent synopsis of the situation, I applaud you on basing your thread on stats and not rhetoric. Kudos.

[ChairmanHal]

Excellent synopsis of the situation, I applaud you on basing your thread on stats and not rhetoric. Kudos.

 

May or may not have been at one point.  The OP was in fact just a snap shot.  But going on now the third round of combat for many, those numbers have no doubt changed.  Also, DH has taken to shipping off its higher end nations to false flags since (if not before actually), so unless you include all those in their total, you are missing a significant number of nations sitting in and out of PM.

[King Louis the II]

May or may not have been at one point.  The OP was in fact just a snap shot.  But going on now the third round of combat for many, those numbers have no doubt changed.  Also, DH has taken to shipping off its higher end nations to false flags since (if not before actually), so unless you include all those in their total, you are missing a significant number of nations sitting in and out of PM.

 

QFT....

 

I actually don't recall a war where changing flags was used as extensively as this one. I am still not sure whether it really makes any difference.

[Saladjoe]

May or may not have been at one point.  The OP was in fact just a snap shot.  But going on now the third round of combat for many, those numbers have no doubt changed.  Also, DH has taken to shipping off its higher end nations to false flags since (if not before actually), so unless you include all those in their total, you are missing a significant number of nations sitting in and out of PM.

Sure they've changed, doesn't take away from the overall initial analysis. And it's really not that hard to follow people that have AA switched, if you know what you're doing.